Block Krylov subspace methods for functions of matrices
نویسندگان
چکیده
منابع مشابه
Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
The Progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank skew-Hermitian part. We analyze this algorithm, observing a critical instability that makes the method unsuitable for some problems. To work around this issue we introduce a diff...
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To approximate f(A)b—the action of a matrix function on a vector—by a Krylov subspace method, restarts may become mandatory due to storage requirements for the Arnoldi basis or due to the growing computational complexity of evaluating f on a Hessenberg matrix of growing size. A number of restarting methods have been proposed in the literature in recent years and there has been substantial algor...
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Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...
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Abstract. This paper presents a modification of Krylov subspace spectral (KSS) methods, which build on the work of Golub, Meurant and others, pertaining to moments and Gaussian quadrature to produce high-order accurate approximate solutions to variable-coefficient time-dependent PDEs. Whereas KSS methods currently use Lanczos iteration to compute the needed quadrature rules, our modification us...
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ژورنال
عنوان ژورنال: ETNA - Electronic Transactions on Numerical Analysis
سال: 2018
ISSN: 1068-9613,1068-9613
DOI: 10.1553/etna_vol47s100